AI 中文总结
本文针对亏格至少3且至多1个边界分支的紧连通定向曲面的一般Kauffman括号skein代数，通过证明其不存在单位特征而Santharoubane构造的对应代数存在增广特征，给出了Santharoubane猜想的反例。
AI 中文摘要
设Σ为亏格至少为3且至多有一个边界分支的紧连通定向曲面。Santharoubane将映射类群模其中心的某些表示与一个有限表现代数关联，该代数带有一个典范满射，对应到Σ的一般Kauffman括号skein代数，他猜想通过合适选择可得到与该skein代数同构的代数。我们证明，该构造得到的每个代数都存在增广特征，而Σ的一般skein代数在ℚ(A)上不存在单位特征；后一结论源于相交1的Dehn扭转恒等式与4孔球面skein关系。因此，所述同构并不成立。
英文摘要
Let $Σ$ be a compact connected oriented surface of genus at least $3$ with at most one boundary component. Santharoubane associated to certain presentations of the mapping class group modulo its center a finitely presented algebra equipped with a canonical surjection onto the generic Kauffman bracket skein algebra of $Σ$, and conjectured that a suitable choice yields an algebra isomorphic to the skein algebra. We show that every algebra arising from this construction admits an augmentation character, whereas the generic skein algebra of $Σ$ admits no unital character over $\mathbb Q(A)$. The latter obstruction follows from the intersection-one Dehn-twist identity together with a $4$-holed-sphere skein relation. Consequently, the conjectured isomorphism does not hold as stated.
Comments12 pages
